俄罗斯新西伯利亚大学“几何、拓扑及其应用”学术报告——Global surfaces of section for Reeb flows on closed 3-manifolds.
发文时间：2022-03-28
来源：304am永利集团
Speaker: Marco Mazzucchelli (Lyon, France)
Time: March 28 (17:00 Beijing time, 16:00 Novosibirsk time).
Abstract: In this talk, which is based on joint work with Gonzalo Contreras, I will sketch a proof of the existence of a global surface of section for any Reeb vector field of a closed 3-manifold satisfying the Kupka-Smale condition. This result implies the existence of global surfaces of section for the Reeb vector fields of C^\infty-generic contact forms on any closed 3-manifold, and for the geodesic vector fields of C^\infty-generic Riemannian metrics on any closed surface. I will discuss a few significant applications of this existence result, and in particular a confirmation of Palis-Smale's stability conjecture for geodesic flows of surfaces: any C^2-structurally stable Riemannian geodesic flow of a closed surface must be Anosov.
Bio: Marco Mazzucchelli am a CNRS researcher at the Unité de Mathématiques Pures et Appliquées of the École normale supérieure de Lyon. His main research interests are dynamical systems, Riemannian geometry, and symplectic topology. He is also co-coordinator of the ANR CoSyDy (Conformally Symplectic Dynamics beyond symplectic dynamics), and member of the ANR Cosy (New challenges in symplectic and contact topology). Mazzucchelli is an editorial board member of the Journal of Fixed Point Theory and Applications.
